WO1999066684A1

WO1999066684A1 - Device, system and method for modem communication utilizing dc or near-dc signal suppression

Info

Publication number: WO1999066684A1
Application number: PCT/US1997/018547
Authority: WO
Inventors: Guozhu Long; Gunnar Holm
Original assignee: Cirrus Logic, Inc.
Priority date: 1996-10-16
Filing date: 1998-06-10
Publication date: 1999-12-23
Also published as: US5926505A

Abstract

Modem technology is implemented in a system including a personal computer (PC) to enable communication over a PSTN using communication software which includes a DC and near-DC signal suppressor.

Description

DEVICE, SYSTEM, AND METHOD FOR MODEM COMMUNICATION UTILIZING DC ORNEAR-DC SIGNAL SUPPRESSION

1. Field of the Invention

This invention relates generally to a modem device, modem-based system and method for signal communication, and more particularly to high speed modem communication utilizing dc or near-dc signal suppression.

2. Background of tlie Invention

Certain known conventional modem devices, systems and methods communicate signals between personal computers (PCs) through public switched telephone networks (PSTNs). However, DC and near-DC (very low frequency) signals cannot pass through some analog circuitry utilized by various conventional modems. [These DC and near-DC signals generate random signals which are transmitted with the transmission signals. The transmission and random signals are received by a modern^ It is therefore desirable to suppress DC and near-DC signals at the transmitting modem.

One method for suppressing DC signals is to apply conventional high-pass filtering techniques, however filtering increases the number of bits required to represent a signal as opposed to a nonfiltered signal. For instance, one of the simpler filters for suppressing DC signals is a first-order differential encoder (1- z^"l) which has a zero at DC Another simple filter is a second order differential encoder (l-z^~2) which has one zero at DC and another zero at 4kHz. However, differential encoders double the dynamic range, which costs 1 bit/ symbol or 8 kbps. Thus, there remains a need for a device or method for suppression of DC or near-DC signals in transmitted signals through modem-connected systems. SUMMARY OF THE INVENTION

In accordance with the present invention, a PC for transmitting and receiving signals over a PSTN utilizes a sign-based device to suppress DC or near DC signal components. The PC includes a modem that communicates with a device, such as another PC, minicomputer, mainframe computer, FAX machine, over the PSTN. The modem includes a DC signal suppressor which applies a sign bit to selected, transmitted digital signal segments prior to analog conversion.

BRIEF DESCRIPTION OF THE DRAWINGS

FIGURE lA is a block diagram of a PC communication system utilizing public switched telephone networks according to the present invention.

FIGURE IB is a block diagram of a PC according to the present invention.

FIGURE 1C is a transmittal signal spectrum according to the present invention.

FIGURE 2 is a block diagram of a 56k!baudmodem communication system according to the present invention.

FIGURE 3 is a block diagram of a[coded encodejj for a 56kjbaudlmodem communication system according to the present invention.

FIGURE 4 is a block diagram of ajp. uncoded encoder] for a Sόk^baudjmodem communication system according to the present invention. FIGURE 5 is a block diagram of a coded encoder with spectrum shaping for a 56k baud modem communication system according to the present invention.

FIGURE 6 is a block diagram of an uncoded encoder with spectrum shaping for a 56k baud modem communication system according to the present invention.

FIGURE 7 is a block diagram of an analog side, half duplex modem receiver according to the present invention.

FIGURE 8 is a block diagram of an alternative embodiment of an analog side, half duplex modem receiver according to the present invention.

FIGURE 9 is a block diagram of an analog side, full duplex modem receiver according to the present invention.

FIGURE 10 is a block diagram of an alternative embodiment of an analog side, full duplex modem receiver according to the present invention.

FIGURE 11 is a block diagram of an alternative embodiment of an analog side, full duplex modem receiver according to the present invention.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIGURE 1 A, an implementation according to the present invention is shown in which PC 100 includes modem 101 and communicates with device 102, such as another PC, minicomputer, mainframe computer, FAX machine, over PSTN 103. Modem 101 may operate at a digital signal transmission/reception rate of 14,400 (14.4k), 28,800 (28.8k), 33,600 (33.6k), 56,000 (56k),[or some other signal rate (referred to as baudπand includes DC suppressor 104 which operates byjapplyingja sign bit (to transmitted digital signal Begmentsjprior toianalog conversionL

Referring to FIGURE IB, PC 100 includes PC system software 105 and PC modem software 106 connected to central processor unit (CPU) 107 through conventional data and instruction bus 108. Modem software 106 is operated by CPU 107 to coordinate the operation of modem controller (not shown) and direct the transmission of signals through modem 106. During operation of modem software 104 by CPU 107, digital signals, which may correspond to a screen image in the case of a data signal transmission or a block of speech in the case of an audio signal transmission, are generated and ordered in digital signal iframes within modem lOlr Each frame contains information associated with N symbols and is defined by K binary bits. The K binary bits are ordered in a digital signal stream and divided into segments.)

x. The binary bits denning each symbol may correspond to a positive or negative value, which in turn will correspond to a positive or negative amplitude when converted to an analog signal. For transmission of each frame, the associated analog signals may be balanced about a 0 voltage to some degree by dividing the symbols being transmitted into groups, such as four, determining the sign of the binary bits associated with each of the first three symbols, determining whether there are more positive than negative signs, and forcing the sign of the binary bits associated with the fourth symbol to balance the preceding signs about neutral which results in a suppression of DC or near- DC digital signal components. To reduce the cost of spectrum shaping, the following steps may be taken. In every 4 symbols, the first 3 symbols are generated as usual. A running sum of all the previously sent symbols. If the running sum is negative, drive the 4th symbol to a positive value; and vise versa. Namely, the sign bit of every 4th symbol is not taken from the user data, but used to suppress DC and very low frequency components. Therefore, the cost is only 1/4 bit/symbols, i.e., 2 kbps in data rate. In the receiver, this sign bit is simply discarded. The transmitted signal spectrum is shown in FIGURE 1C.

From this example, it may be noted that to put some constraints upon the signal spectrum, some redundancy has to be added. The approach discussed above can be generalized. The data symbols can be divided into frames of size N. In the encoder, check the N symbols in a buffer in each frame and do some transform on these symbols to change the unwanted frequency components into some good frequencies; and use M bits in the beginning of each frame to inform the remote receiver which one out of 2^M possible transforms has been used for this frame so that the receiver can do the inverse transform to recover the original data symbols. One example is to multiply the data symbol sequence x(i) by a sign transform sequence s(i) consisting only a value +1 or -1 to generate the output sequence y(i)=x(i)s(i). In the receiver, x(i) is recovered from y(i) by x(i)=y(i)s(i). 2^M proper transform sequences may be implemented to effectively transform the unwanted frequencies into good ones. The cost of such a scheme is M/N bit/symbol. For example, if N=32 and M=3, the cost is 3/32 bit/symbol, i.e., 750 bps.

Referring to FIGURE 2, a 56k baud modem communication system is shown connecting digital modem 101 through PSTN 103 to analog modem 201 connecting to device 102. The sampling rate is 8 kHz. At each sample, a set of input bits operated upon by a scrambler (not shown). The scrambler output is used by an encoder (not shown) to generate output digital samples. These samples are sent through digital network 203 to μ-law D/ A 205 and converted into analog signals.

μ-law D/ A 205 uses a sign-magnitude format with a total of 255 possible input digital values. Those 255 values are divided into 16 segments: +l,+2,...+8,- 1,-2,... -8. The distance between two adjacent points in the i-th segment is c*2"^'υ. For simplicity in discussion but not limiting the value thereto, consider c=l. Segments +1 and -1 have the smallest distance 1, and the point 0 is shared by both segments. These two segments with the smallest distance may be excluded without a significant loss in transmission or reception quality, leaving 224 points. Note that a next smaller pair of points may be excluded and so forth in order to increase the smallest distance. For every 32 points excluded, the smallest distance is doubled, with a resulting gain of 6 dB noise margin.

Among all the points that are useable in signal transmissions, the outer points have the largest distances and are the preferred points for utility.

In order to use the larger points more often, a conventional shell mapping algorithm may be modified and applied. For instance, a conventional V.34 modem divides the 2-dimensional signal constellation into M rings each of which has the same number of points. These M rings are ordered based on the averaged power in the ring. The shell mapping algorithm chooses the inner rings more often to reduce the total averaged power.

In the present invention, the one-dimensional points are divided into 2m segments: ±(9-m), ...,±7,±8, m=l,2,...7. The +i and -i segments are merged into one segment with segment index 8-i. The segment index is ordered from the largest energy to the smallest energy.

Referring to FIGURE 3, encoder 301 is shown connected to digital network 203 and receiving multiple inputs. Encoder 301 includes segment mapper 303 and trellis encoder 304 which both provide input signals to bit map 305. Upon encoding the transmittal signals, encoder 301 transmits from bit map 305 onto digital network 203.

Now, more specifically, by selecting M useable points and transmitting bits in a frame of N symbols, the data rate is 8000 /N bits /sec. The M points are divided into m=M/32 segments 0,l,...m-l. Note that neither K/N, which is the bit per symbol, nor K are required to be integers. A frame switch technique may be applied for non-integer K cases. However, for simplicity of discussion, assume K to be an integer. If 5 bits are required to select a point within a segment, k=K-5N bits may be used to do "segment mapping". The largest possible k can be found from the following inequality: 2^k<m^N. For example, if 192 points are used and the mapping frame size is 8, then m=6, and k<20.68. If a value of k=20 is used, 7.5 bits per symbol are transmitted, and the data rate is (k+5N)*8000/N=60 kbps.

To send signalling information, one bit is conventionally used (robbed) in every 6 symbols, however some older codecs use one bit from each symbol. Therefore, one bit out of every six symbols, the LSB is left for the robbed signaling bit, leaving M/2 possible points for usage, however it may be noted that the invention may be modified to accommodate the older codec requirements. With M/2 possible points, 4 bits may be used to choose an even point. The data rate is then reduced by 8000/6=1333.33 bps. For some old codecs, the robbed signaling bit is used in every symbol, and thus the data rate is reduced by 8 kbps.

The largest possible k is not required to be used. If a small k is used, some "distance gain" may be obtained since there is freedom to use outer points.

If a value of N=8 is selected, then the segment mapping algorithm applied may be the same as the shell mapping algorithm utilized in conventional V.34 modems. In the shell mapping algorithm, the cost function is approximated by a linear function which is a good approximation to minimize the averaged power but not average distance.

If a criterion is to minimize the averaged distance, then the ideal cost function should be inversely proportional to the distance, which is an exponential function. For instance, if 7 segments are used, choosing two segment 5 points, one segment 4 point and one segment 6 point results in the same cost if a linear cost function is used, however the average distances are 128 and (256+64)/2=160, respectively. Ideally, the mapping algorithm should therefore be modified so that the maximum average distance can be obtained.

In one alternative for a shell mapping algorithm, suppose there are 7 rings, a generating function may be implemented as follows:

gl=l+x+x²+ x³+ x⁴+ x⁵+ x⁶. g2=gl*gl=l+2x+3x²+ 4x³+ 5x⁴+ 6x⁵+ 7x⁶+6x⁷+5x⁸+4x⁹+3x¹⁰+2x^π+x¹² g4=g2*g2=l+... x²⁴ g8=g4*g4=l+... x⁴⁸

The G4 table size is 4m-4 and the G8 table size is 8m-8, where m is the number of rings.

Now, if k=7, modify the cost function to 0,1,2,4,8,16,32 and the generating function becomes: gl=l+ x+x²+x⁴+ x⁸+ x¹⁶+ x³². g2=gl*gl=l+2x+2x³+ 2x⁵+ 2x⁶+ 2x⁸+ 2x⁹+ 2x¹⁰+2x¹ +2x¹⁶+....+2x⁴⁰+2x^4θ+x⁶⁴ g4=g2*g2=l+... x¹²⁸ g8=g4*g4=l+... x²⁵⁶

The G4 table size is 1+2" and the G8 table size is l+2^k+1, although there are some zeros.

The same mapping algorithm can be used, but the tables are much bigger, and the complexity is higher.

On the other hand, the large average distance may not be the only criterion. An alternative criterion is to minimize the frequency of the smallest segment. Since the errors are most likely in the smallest segment, this criterion may yield improved results. In order to obtain this result, the generating function may be implemented as: gl=l+x+x²+ x³+ x + x⁵+ x⁴¹. In this case, any 8-point combination with at least one point in the smallest segment has a higher cost than all the 8-point combinations without any point in the smallest segment. In other words, the smallest segment is chosen only after all the combinations without that segment are used. As an extreme case, if the minimum frequency of the smallest distance is the only criterion, a simpler generating function may be implemented as: gl=6+x

In this case, the cost function is 0,0,0,0,0,0,1 and only the smallest segment should not be used.

Another alternative criterion may be to reduce the use of the second smallest segment. This criterion may be obtained by implementing the following generating function: gl=5+x+ x⁹

In this case, the cost function is 0,0,0,0,0,1,9 and only the smallest 2 segments should not be used. The table size is reasonable, and the performance may be slightly better than the above alternative embodiment.

If one of these cost functions is used, the cost is not simply the segment index. For instance, if the last cost function is used, cost 0 means segment 0 to 4, cost 1 means segment 5 and cost 9 means segment 6. In such a case, the segment which should be used may be determined by implementing a secondary generating function. Similar to the shell mapping algorithm above, the Z8 table is searched to find the total cost of 8 symbols. If the total cost is 0, a secondary generating function may be implemented as:

hl=l+x+x²+ x³+ x⁴ h2=hl*hl h4=h2*h2

Then using the same mapping algorithm, 8 segment indices may be obtained ranging from 0 to 4.

If the total cost of 8 symbols is not zero, continue to use the g4 table to split the cost of 8 into 2 costs of 4 symbols. If one of the 4-cost is zero, switch to the h2 table to obtain 4 segment indices from 0 to 4. Similarly, if the 4-cost is not zero, continue to use the g2 table to split the 4-cost into two 2-costs. If one of the 2-cost is zero, use hi to obtain 2 segment indices. Note that the h tables are very small.

From "segment mapping", 8 segment indices(from 0 to m-1) are obtained. Index 0 means actual segment +8 and -8, with a total of 32 points. Five bits are then used to pick one of these 32 points. For the 6th symbol, due to the LSB being the robbed signaling bit, use only 4 bits to choose one of the 16 points.

Trellis code is a power technique to improve the performance. Using trellis coder 304, a 4D code may be used such as in V.34 modems. Symbols are one dimensional and four symbols may be combined as a 4D signal, and applied to the 4D code. The cost is one bit every 4D, i.e., 0.25 bit per symbol, or 2 kbps. In every 4 symbols, input 3 coding bits and generate 4 bits for selecting subset, possibly 1 bit for each symbol as the LSB to select between even and odd points. In such cases, there are k+27.5 bits per mapping frame. In the above example, k=15 and the data rate is 56.67 kbps.

Special consideration should be given to the robbed signaling bit in every 6th symbol as to how to do the Trellis code, since the robbed bit is also at the LSB, which selects between even and odd points. One possible solution is to use the coding bit as the bit 1 for the symbols with bobbed bit, namely, for that particular symbols, the signal distance is doubled. The Viterbi decoder will slice the signal differently for that symbol. In that case, there is a 1333 bps loss in data rate.

Note that the robbed signaling bit affects the selection of points within the segment, and does not affect the segment mapping itself. Therefore, the mapping frame size does not have to be 6. For example, the above-mentioned shell mapping algorithm may be used with the same mapping frame size 8.

The parser for a 1/6 robbed signaling bit is as follows. Define a large frame having 24 symbols, i.e., 3 mapping frames with 8 symbols each, or 6 coding frames with 4 symbols each. In the ith large frame, there are 3k segment mapping bits, 18 coding bits, and 92 uncoded bits.

The data rate is (k+36.67) kbps for 1/6 robbed signaling bit. The data rates for different M values are listed in the following table.

M m distance k date rate(kbps) data rate for fully robbed

224 7 2 22 58.67 52

192 6 4 20 56.67 50

160 5 8 18 54.67 48

128 4 16 16 52.67 46

96 3 32 12 48.67 42

64 2 64 8 44.67 38

32 1 128 0 36.67 30

Table 1. Data rates versus M values.

For the fully robbed signaling bit case, the parser is simpler. The period is one mapping frame.

^<I,1A2'

There are k segment mapping bits, 6 coding bits, and 24 uncoded bits in every mapping frame of 8 symbols. The data rate is (k+30) kbps. For different M values, the data rates are listed in the above table.

From the table, it may be noted that to support a 56k baude data rate, only 192 points are required, and the smallest distance is 4. Hence, about a 40 dB SNR is required for reasonable performance. Consider the segment mapping gain and coding gain, 36 dB SNR may be enough. This requirement is certainly not be too difficult to meet. If the loop does not support this requirement, reduce M to 160. Then with 30 dB SNR, a 54.67 kbps data rate may be run.

From the table, it may also be noted that k is typically reduced by 2 and the data rate is reduced by 2 kbps if m is reduced by 1. Reducing m by 1 provides a 6 dB noise margin. Therefore, instead of using coding, reduce m by 1 to get the same data rate with a better noise margin and simpler implementation of encoder 401 as shown in FIGURE 4. The following table lists the data rates for an uncoded case.

M m distance k date rate(kbps) SNR required

224 7 2 22 60.67 46

192 6 4 20 58.67 40

160 5 8 18 56.67 34

128 4 16 16 54.67 28

96 3 32 12 50.67 22

64 2 64 8 46.67 16

32 1 128 0 38.67 10

Table 2. Data rates for an uncoded implementation

It may be noted that the conventional convolutional code is not efficient, which may be due in part to the uneven signal distribution. In outer segments, the signals are so far apart that coding is not needed. Only the smallest segment needs help. An efficient step is to add redundancy only at the smallest segment.

The hybrid transformers have spectral null at DC, but the random data signal has a flat spectrum from 0 to 4 kHz. It is desired that the transmit signal does not have DC and very low frequency components.

To eliminate the DC component, as discussed above, alternative embodiment of encoders 501, 601, coded and uncoded respectively, are shown in FIGURES 5 and 6 which includes DC suppressor (spectrum shaper) 503 for shaping the spectrum. Every 4 symbols, the first 3 symbols are generated as usual. A running sum of all the previously sent symbols is maintained. If the running sum is negative, the 4th symbol is made positive; and vise versa. In this way, the DC signal and very low frequency components are suppressed. Overall, for random input data, the probabilities for the fourth symbol to be positive and negative are the same.

With this scheme, the data rate table becomes the following.

M m distance k date rate(uncoded) data rate(coded)

224 7 2 22 58.67 56.67

192 6 4 20 56.67 54.67

160 5 8 18 54.67 52.67 128 4 16 16 52.67 50.67

96 3 32 12 48.67 46.67

64 2 64 8 44.67 42.67

32 1 128 0 36.67 34.67

Table 3. Date rate with DC suppressor.

It may be noted that 56 kbps is still possible.

It is also possible to increase M by 16 while keeping the smallest distance the same. Specifically, every other point may be used in the smaller segment. For example, 16 points may be used in segment 2 together with 192 points in segment 3 to 8, and keep the smallest distance 4. To use the mapping algorithm, the number of points in each group should be the same. Hence, divide the total of M points into m=M/16 group, i.e., one normal segment is divided into 2 groups, and the smallest segment, which has only half the points, has only 1 group. Now, m ranges from 1 to 15. We use 4 bits to choose one point from each group. By using more points, the data rate may be increased typically by 1 or 2 kbps. In the mapping algorithm, the generating function for odd m can be:

gl=(m-3) + 3x; hl=l+χ+χ²+...+χ^m"4; or gl=(m-5) + 2x + 3x⁹, hl=l+x+x²+...+x^m"6;

A data rate table of the corresponding performance is shown below:

M m distance k date rate (uncoded) data rate(coded)

240 15 2 31 59.67 57.67

224 14 2 30 58.67 56.67

208 13 4 29 57.67 55.67

192 12 4 28 56.67 54.67

176 11 8 27 55.67 53.67

160 10 8 26 54.67 52.67

144 9 16 25 53.67 51.67

128 8 16 24 52.67 50.67

112 7 32 22 50.67 48.67

96 6 32 20 48.67 46.67

80 5 64 18 46.67 44.67 64 4 64 16 44.67 42.67

48 3 128 12 40.67 38.67

32 2 128 8 36.67 34.67

16 1 256 0 28.67 26.67

Table 4. Data rate using reduced points

With reference again to FIGURE 2, the 64 kb/s digital signal goes through digital network 203, and is then converted into analog signal through μ-law D/A converter 205. This analog signal goes through the analog local loop and arrives at 56k analog modem receiver 201.

With reference to FIGURE 7, half duplex, analog 56k modem receiver 701 is shown. The analog signal from the local loop is converted to digital by a linear A/D converter. Since it is not easy to perfectly control the input analog signal level and sampling clock, a μ-law A/D is not implemented at this location. Instead, a linear A/D converter is used and the μ-law to linear conversion is done after subtracting DC, AGC, interpolator and equalizer. The equalizer output should match the linearly-quantized signal of the μ-law D/A output at the local central office. The equalizer output is converted by μ-law to linear conversion to obtain the digital signal sent in the network. After the decoder (Viterbi decoder for coded version and simple slicer for uncoded version) decodes the received signal, the segment mapping decoder operates to obtain the k mapping bits. The robbed signaling bit and spectrum shaping bit are removed, and the descrambler operates to obtain the user data.

The equalizer runs at an 8k sampling rate, hence for a span of 40 symbols, about 96 taps are required. Since only one local loop has to be equalized, the span may be reduced. However, since the signal spectrum is wider and the channel has a null at DC and high attenuation near 4kHz, a relatively long span may be necessary.

To avoid noise enhancement by the linear equalizer, decision feedback equalizer can be used, especially when coding is not used, and thus decoding delay is not eliminated. The decision feedback equalizer is shown in FIGURE 8. With reference to FIGURE 9, full duplex, 56k modem 801 is shown. The 56k transmission as discussed above is only in the direction from digital to analog. In the other direction, a less radical operation is required.

Note that since there is no near echo, therefore only a far echo canceller is required. The input to the echo canceller is the real transmitted signal which does not have a flat spectrum, if spectrum shaping is used. This may affect the initial convergence speed. Both the input and the output sampling rate of the far echo canceller are 8k. Since the transmitted signal is real with only 8 bit precision, we can use one word for 2 samples in the far echo bulk delay line. For 1.2 second round trip delay, the bulk delay line needs 4.8k words. 96 taps may be used for the far echo canceller for a time span similar to that in a V.34 far echo canceller at 3429 baud rate. Note that the input delay line needs also 96 words.

Automatic gain control (AGC) and demodulation are performed after the echo cancellation. A 1:2 upsampler is used before the interpolator to increase the sampling rate to 16kHz. A baseband 3rd order sine interpolator can be used for both the 16k to 3x conversion and the timing recovery at the same time. After the interpolator, the devices and operations are conventional.

One of the disadvantages of this structure is that the demodulation is done at an 8kHz sampling rate. This makes the sine/cosine table used for the demodulator very long. To avoid this problem, an alternative embodiment is shown in FIGURE 10.

After AGC, a 1:3 upsampler may be used to increase the sampling rate to 24k. The passband sampling rate conversion and timing recovery are followed by a 3x demodulator, which requires much shorter sine/cosine tables.

With reference to FIGURE 11 wherein duplex modem 1101 is shown. Note that since the 56k received signal uses the sampling clock 8 kHz, and its spectrum is up to 4 kHz, the down sampler output rate has to be >8kHz. A 3x rate is acceptable except at 2400 baud, where 4x should be used. But at 2400 baud, a smaller number of taps may be used for each subcanceller. For example, 40 taps in each subcanceller may be used for all the other baud rates, and only 30 taps for 2400 baud, so the total number of taps is still 120.

After the echo cancellation, and AGC, an upsampler is used to get mnx sampling rate. This upsampler is necessary because the 8k sampled received signal has a spectrum from -4kHz to 4kHz, which is much wider than that of the baseband 3x V.34 signal. For a 3rd order sine interpolater, m=3 seems appropriate. A baseband 3rd order sine interpolator can be used for both the mnx to 8k conversion and the timing recovery at the same time.

Claims

What is claimed is:

1. A modem device for transmission and reception of data over a network comprising: a near-DC signal suppressor for removing low frequency components of a transmission signal spectrum.

2. A modem communication system for communication of data over a a network medium through a personal computer, comprising:

at least two devices connected to the network medium at spaced locations;

one of the two devices comprising a personal computer having

a digital modem for communication of digital data over the network medium, the digital modem including a near-DC signal suppressor for removing low frequency components of a transmission signal spectrum,

another of the two devices having

an analog modem for reception of analog data from the network medium.

3. A method for transmitting digital data over a network including the step of:

suppressing the low frequency components of the transmission signal spectrum.